Sunday, 1 January 2017

general relativity - Is this analogy of Hawking Radiation correct?


Through reading of textbooks and other research papers, I have settled on the analogy of hawking radiation below (Written completely by myself)



Within the ergosphere of the black hole, virtual pairs of particles and anti-particles are constantly appearing due to vacuum fluctuations. Typically, the pair would then annihilate before this could be of any consequence. However, as one of these two particles will be closer to the hole than the other, it will experience a greater gravitational force than the other. Thus, there is the possibility that one particle will fall into the black hole while the other escapes to infinity. The particle that falls in will have negative energy, and subsequently negative mass, leaving the positive energy particle outside of the hole.


It is not the black hole that is directly emitting the particle, but from an external reference frame, this appears to be case. As tidal forces are greater for smaller black holes, the rate of emission of Hawking radiation increases as the hole decreases in size. In an isolated system, this would lead to an exponential decay. However, black holes are constantly accreting mass too. As such, any black hole with a sufficient mass will accrete mass faster than it loses it via Hawking radiation. Yet this is not the case with smaller holes, which would slowly ’evaporate’.



As this is all outside of my school curriculum and way above my current level of taught physics, I was hoping someone could either confirm that my analogy is correct or provide some constructive criticism and advice. Thanks!



Answer



As the comments have suggested, the problem is that your description of virtual particles appearing to vacuum fluctuations is wrong. Have a look at my answer to Black holes and positive/negative-energy particles for more on this.



There isn't an explanation of what is really going on that is accessible to the non-quantum field theory nerd (though I have attempted one in the answer I've linked above). No-one seems to know exactly where the pairs of virtual particles analogy came from because it doesn't correspond to the current day descriptions of the quantum vacuum. In any case virtual particles are more of a computational device than anything real. The best article I've seen on this is this one on matt Strassler's blog.


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